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Approximating combinatorial optimization problems with the ordered weighted averaging criterion

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  • Chassein, André
  • Goerigk, Marc
  • Kasperski, Adam
  • Zieliński, Paweł

Abstract

This paper deals with combinatorial optimization problems with K cost scenarios, inducing K linear objectives. The popular Ordered Weighted Averaging (OWA) criterion is used to aggregate the objectives and compute a solution. It is well-known that minimizing OWA for most basic combinatorial problems is weakly NP-hard even if the number of scenarios K equals two, and strongly NP-hard when K is a part of the input. In this paper, the problem with nonincreasing weights in the OWA criterion and a large K is first considered. A method of reducing the number of scenarios, by appropriately aggregating the costs before solving the problem, is proposed. It is shown that an optimal solution to the reduced problem has a guaranteed worst-case approximation ratio. Some new approximation results for the Hurwicz criterion, which is a special case of OWA, are also presented.

Suggested Citation

  • Chassein, André & Goerigk, Marc & Kasperski, Adam & Zieliński, Paweł, 2020. "Approximating combinatorial optimization problems with the ordered weighted averaging criterion," European Journal of Operational Research, Elsevier, vol. 286(3), pages 828-838.
    • Handle: RePEc:eee:ejores:v:286:y:2020:i:3:p:828-838
    DOI: 10.1016/j.ejor.2020.04.018
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    References listed on IDEAS

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    Cited by:

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    2. Mahmoud Kiasari & Mahdi Ghaffari & Hamed H. Aly, 2024. "A Comprehensive Review of the Current Status of Smart Grid Technologies for Renewable Energies Integration and Future Trends: The Role of Machine Learning and Energy Storage Systems," Energies, MDPI, vol. 17(16), pages 1-38, August.

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